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Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem

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Abstract

In this paper we will present the local stability analysis and local error estimate for the local discontinuous Galerkin (LDG) method, when solving the time-dependent singularly perturbed problems in one dimensional space with a stationary outflow boundary layer. Based on a general framework on the local stability, we obtain the optimal error estimate out of the local subdomain, which is nearby the outflow boundary point and has the width of \(\mathcal {O}(h\log (1/h))\), for the semi-discrete LDG scheme and the fully-discrete LDG scheme with the second order explicit Runge–Kutta time-marching. Here \(h\) is the maximum mesh length. The numerical experiments are given also.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu Province, China

    Yao Cheng, Feng Zhang & Qiang Zhang

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  1. Yao Cheng
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  2. Feng Zhang
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  3. Qiang Zhang
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Correspondence to Qiang Zhang.

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Research supported by NSFC grant 11271187.

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Cheng, Y., Zhang, F. & Zhang, Q. Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem. J Sci Comput 63, 452–477 (2015). https://doi.org/10.1007/s10915-014-9901-6

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  • DOI: https://doi.org/10.1007/s10915-014-9901-6

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